Physics Informed Neural Network Code for 2D Transient Problems (PINN-2DT) Compatible with Google Colab

TL;DR

An open-source Physics Informed Neural Network environment for simulations of transient phenomena on two-dimensional rectangular domains, compatible with Google Colab and automatically differentiates PINN with respect to spatial and temporal variables is presented.

Abstract

We present an open-source Physics Informed Neural Network environment for simulations of transient phenomena on two-dimensional rectangular domains, with the following features: (1) it is compatible with Google Colab which allows automatic execution on cloud environment; (2) it supports two dimensional time-dependent PDEs; (3) it provides simple interface for definition of the residual loss, boundary condition and initial loss, together with their weights; (4) it support Neumann and Dirichlet boundary conditions; (5) it allows for customizing the number of layers and neurons per layer, as well as for arbitrary activation function; (6) the learning rate and number of epochs are available as parameters; (7) it automatically differentiates PINN with respect to spatial and temporal variables; (8) it provides routines for plotting the convergence (with running average), initial conditions learnt, 2D and 3D snapshots from the simulation and movies (9) it includes a library of problems: (a) non-stationary heat transfer; (b) wave equation modeling a tsunami; (c) atmospheric simulations including thermal inversion; (d) tumor growth simulations.

Figures (13)

• Figure 1: Heat equation. Convergence of the residual loss function.
• Figure 2: Heat equation. Running average from the convergence of the residual loss function.
• Figure 3: Heat equation. Initial conditions in 2D.
• Figure 4: Heat equation. Initial conditions in 3D.
• Figure 5: Heat equation. Snapshot from the simulation.